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2 years ago

I don't know how to do this

Mathematics

1 answer:

Artemon [7]2 years ago

3 0

Answer:

i dont ethier ;i

Step-by-step explanation:

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A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(

alekssr [168]

Answer:

$\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right)$ or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

$\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1$

Set $f'(x)$ equal to 8/7 and solve for x:

$\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}$

Therefore, $f(x)$ will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into $f(x)$ to get the y-coordinate:

$\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}$

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

5 0

2 years ago

Expand (2x+2)^6<br> How would you find the answer using the binomial theorem?

Yanka [14]

Answer:

Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

. Of the 200 students surveyed in 5th grade, 120 prefer bananas and 80 prefer apples. what is the part to whole ratio?

kaheart [24]

120:200 prefer bananas, 80:200 prefer apples

7 0

3 years ago

Two accountants for the firm of Elwes and Wright are arguing about the merits of presenting an income statement in a multiple-st

olchik [2.2K]

Answer:

73,188

Step-by-step explanation:

fees plus costs minus expenses

8 0

3 years ago

/ why we use this symbol

user100 [1]

The slash is an oblique slanting line punctuation mark /. Once used to mark periods and commas, the slash is now most often used to represent exclusive or inclusive or, division and fractions, and as a date separator.

5 0

2 years ago